Not really. You're coarse graining either way, it's just a matter of feature selection and atomicity. But more relevantly, my point was that the only reason we don't experience things like the "chaos" of celestial bodies smashing into one another on earth is because, well...it's earth. There's only one celestial body here, and that's earth.
But if you're looking at cosmic catastrophes, asteroid collisions, and so forth as indicative of a type of chaos we don't find on earth, then you can find far more in you're average boiling kettle. Far more collisions with many times the number of bodies. A gram of O2 gas contains something like 2 followed by 22 zeros (~20,000,000,000,000,000,000,000) of molecules. So when boiling water you're talking about many trillion trillion trillion of high speed collisions every second.
That's sort of the point. The collisions referred to (asteroids) only seem chaotic because they are big and because the truly chaotic behavior of systems occurs at smaller (human) scales. You can of course look inside stellar structures and so forth and talk about the many-body problem for solids in general or the subatomic constituents of asteroids and again find that you need trillions upon trillions of equations, but that's unnecessary. We can obtain great accuracy when it comes to celestial bodies if we treat them as point particles (often simply by using the center of mass as the "point"). Doing the same with liquids or gases fails completely and thus we can only ever hope to approximate the behavior of such systems using statistical mechanics.
But truly chaotic systems require a combination of different kinds of interacting components or subsystems, such as in biology or climate. We don't generally find much comparable in astrophysics. Actually, when we can use physics at all, then often the system is relatively simple.
There are in general infinitely many solutions to most systems of equations that have a solution (a golden rule in linear algebra, if you recall, is that if there is a solution then either there is only one or there are infinitely many; things mostly stay the same with differential equations except that the nature of the solution spaces changes dramatically as do the characteristics of the systems). In general, none of the n-body problems have solutions when n is greater than 2. However, this is because the equations don't have closed for analytical solutions in that you can't simply take antiderivatives (indefinite integrals) and solve for arbitrary constants- you need initial conditions and a picture of the system in order to determine how to solve it (or to approximate a solution) by e.g., exploiting symmetries. The three-body problem is special because it is easy to visualize and because there aren't really any mathematical difficulties encountered in e.g., 60-body problems or 100-body problems that aren't already present in the three-body problem. The difference as N increases is that the complexity becomes so great that the approximation schemes (numerical solutions) which work in the three-body case begin to fail and better methods are required. Also, celestial mechanics present special cases precisely because the interactions among bodies are all related to the gravitational force when more generally you have to take into account e.g., electromagnetic forces and in particular collisions. Orbits are relatively easy. Sand, dust, water, gas, cells, etc., are hard or impossible on an entirely different level.